Variable neighborhood search: Principles and applications

Numerous transportation applications as diverse as capital investment decision-making, vehicle fleet planning, and traffic light signal setting all involve some form of (discrete choice) network design. In this paper, we review some of the uses and limitations of integer programming-based approaches to network design, and describe several discrete and continuous choice models and algorithms. Our objectives are threefold—to provide a unifying view for synthesizing many network design models, to propose a unifying framework for deriving many network design algorithms, and to summarize computational experience in solving design problems. We also show that many of the most celebrated combinatorial problems that arise in transportation planning are specializations and variations of a generic design model. Consequently, the network design concepts described in this paper have great potential application in a wide range of problem settings.

Network Design and Transportation Planning: Models and Algorithms

The data stream model has recently attracted attention for its applicability to numerous types of data, including telephone records, Web documents, and clickstreams. For analysis of such data, the ability to process the data in a single pass, or a small number of passes, while using little memory, is crucial. We describe such a streaming algorithm that effectively clusters large data streams. We also provide empirical evidence of the algorithm's performance on synthetic and real data streams.

/pdf/clustering-data-streams-theory-and-practice-438yg20hny.pdf

Clustering data streams: Theory and practice

Linear-time algorithms for linear programming in $R^2 $ and $R^3 $ are presented. The methods used are applicable for other graphic and geometric problems as well as quadratic programming. For exam...

Linear-Time Algorithms for Linear Programming in $R^3 $ and Related Problems

Given n demand points in the plane, the p-center problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demand point to its respective nearest supply point. The p-median problem is to minimize the sum of distances from demand points to their respective nearest supply points. We prove that the p-center and the p-median problems relative to both the Euclidean and the rectilinear metrics are NP-hard. In fact, we prove that it is NP-hard even to approximate the p-center problems sufficiently closely. The reductions are from 3-satisfiability.

/pdf/on-the-complexity-of-some-common-geometric-location-problems-4gvcch5lmf.pdf

On the Complexity of Some Common Geometric Location Problems

It is shown that the problem of finding a p-median of a network is an $NP$-hard problem even when the network has a simple structure (e.g., planar graph of maximum vertex degree 3). However, results leading to efficient algorithms are presented when the network is a tree: In particular, we first show that a 1-median of a tree is identical to its w-centroid, and obtain Goldman’s $O(n)$ algorithm for finding a 1-median of a tree out of more general considerations. Then, we present an algorithm which finds a p-median of a tree (for $p > 1$) in time $O(n^2 \cdot p^2 )$.

O. Kariv

Papers

An Algorithmic Approach to Network Location Problems. II: The p-Medians